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In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…
Ever since Claude Shannon used entropy for his "Mathematical Theory of Communication", entropy has become a buzzword in research circles with scientists applying entropy to describe any phenomena that are reminiscent of disorder. In this…
We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales,…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…
We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable…
We study the chaotic motion of a semi-classical optomechanical system coupled to a non-Markovian environment with a finite correlation time. We show that the non-Markovian environment can significantly enhance chaos, by studying the…
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…
Pesin's identity provides a profound connection between entropy $h_{KS}$ (statistical mechanics) and the Lyapunov exponent $\lambda$ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…
Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknown models to produce a definitive 0--1 diagnostic.…